New Results on the Identification of Normal Modes From Experimental Complex Modes

Balmès, Étienne

doi:10.1006/mssp.1996.0058

Cited by 91 publications

(70 citation statements)

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“…In the same way, the left and right complex vectors should be identical, which is not the case even if the differences are quite small. A better procedure would be to apply the methodology dedicated to symmetric systems which has been presented in [1]. The direct use of the methodology including symmetry constraints gives the following values for the mode shapes and matrices: …”

Section: Resultsmentioning

confidence: 99%

“…This equation is the generalization of the expression in reference [1]. It does not possess a unique solution.…”

Section: Rjmentioning

confidence: 96%

“…The properness condition for the complex modes of symmetrical systems is described in detail in reference [1]. Starting from a given set of 2n identified complex modes, this condition is related to the fact that the system can be exactly represented in the frequency range of interest, by a n-degrees of freedom equivalent physical model, built from the identified modes.…”

Section: Properness Conditionmentioning

confidence: 99%

“…If a set of vectors does not verify the properness condition, this means that either the system can not be represented by this reduced set of modes, or that the experimental identification has introduced errors in the eigenshapes as the properness condition is very sensitive to noise. In this case, Balmès has proposed a methodology to enforce the properness condition in structural dynamics [1]. In the same paper, it is also shown that the properness condition is equivalent to the completeness of the basis, which is discussed for example in references [8] and [9].…”

Section: Properness Conditionmentioning

confidence: 99%

“…It has been shown [1] that for structural dynamics problems with symmetric matrices, the existence of an equivalent physical experimental reduced model is equivalent to the so-called properness condition of complex vectors. Moreover, in this same paper, an efficient methodology has been proposed to enforce that property when identified modes do not verify the properness condition.…”

Section: Introductionmentioning

confidence: 99%

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On the properness condition for modal analysis of non-symmetric second-order systems

Ouisse

Foltête

2011

Mechanical Systems and Signal Processing

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To cite this version:Morvan Ouisse, Emmanuel Foltete. On the properness condition for modal analysis of non symmetric second order systems. Mechanical Systems and Signal Processing, Elsevier, 2011, 25 (2) Emmanuel FOLTÊTE AbstractNon symmetric second order systems can be found in several engineering contexts, including vibroacoustics, rotordynamics, or active control. In this paper, the notion of properness for complex modes is extended to the case of non self-adjoint problems. The properness condition is related to the ability of a set of complex modes to represent in an exact way the behavior of a physical second order system, meaning that the modes are the solutions of a quadratic eigenvalue problem whose matrices are those of a physical system. This property can be used to identify the damping matrices which may be difficult to obtain with mathematical modeling techniques. The first part of the paper demonstrates the properness condition for non symmetric systems in general. In the second part, the authors propose a methodology to enforce that condition in order to perform an optimal reconstruction of the "closest" physical system starting from a given basis complex modes. The last part is dedicated to numerical and experimental illustrations of the proposed methodology. A simulated academic test case is first used to investigate the numerical aspects of the method. A physical application is then considered in the context of rotordynamics. Finally, an experimental test case is presented using a structure with an active control feedback. An extension of the LSCF identification technique is also introduced to identify both left and right complex mode shapes from measured frequency response functions.

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Section: Resultsmentioning

confidence: 99%

“…This equation is the generalization of the expression in reference [1]. It does not possess a unique solution.…”

Section: Rjmentioning

confidence: 96%

Section: Properness Conditionmentioning

confidence: 99%